基于弹塑性梁模型的最大有效力矩准则单元边长定量研究

doi:10.13209/j.0479-8023.2025.034

北京大学学报（自然科学版） ›› 2026, Vol. 62 ›› Issue (3): 571-580.DOI: 10.13209/j.0479-8023.2025.034

基于弹塑性梁模型的最大有效力矩准则单元边长定量研究

刘天乐, 何涛^†

深地探测与矿产勘查全国重点实验室, 造山带与地壳演化教育部重点实验室, 北京大学地球与空间科学学院, 北京 100871

收稿日期:2025-04-09 修回日期:2025-05-01 出版日期:2026-05-20 发布日期:2026-05-20
基金资助:
国家自然科学基金(42174133)资助

Quantitative Study on Unit Length of Maximum Effective Moment Criterion Based on Elastoplastic Beam Model

LIU Tianle, HE Tao^†

SKLab-DeepMinE, The Key Laboratory of Orogenic Belts and Crustal Evolution (MOE), School of Earth and Space Sciences, Peking University, Beijing 100871

Received:2025-04-09 Revised:2025-05-01 Online:2026-05-20 Published:2026-05-20

摘要/Abstract

摘要：

针对最大有效力矩准则的作用范围缺乏定量解释的问题, 基于弹塑性梁模型开展研究。首先, 根据均匀弹塑性梁在纯弯曲状态下的正应力分布解析解, 推导出准则的单元边长近似等于梁的高度。然后, 采用COMSOL有限元软件, 模拟双层和三层弹塑性梁的弯曲屈服过程, 结果表明上述理论关系对叠层梁(代表沉积地层)同样有效。最后, 通过分析梁上近似膝折带塑性变形区域的几何比例关系, 结合野外露头测量膝折带宽度, 定量地估算受该准则控制的地层厚度, 实现最大有效力矩准则中单元边长的定量化。研究结果可为相关地质构造的应力–应变场恢复和变形过程分析提供理论依据。

关键词: 最大有效力矩准则, 弹塑性梁, 膝折带, 有限元方法, COMSOL

Abstract:

Aiming at the lack of quantitative interpretation of the operational scale of the maximum effective moment criterion, this study is carried out based on an elastoplastic beam model. First, using the analytical solution for the normal stress distribution in a homogeneous elastoplastic beam under pure bending, the unit length of the criterion is derived to be approximately equal to the beam height. Subsequently, the bending and yielding process of double- and triple-layer elastoplastic beams are simulated using COMSOL multiphysics software. The results confirm that the above theoretical relationship is also valid for laminated beams (representing sedimentary strata). Finally, by analyzing the geometric scaling relationship of the kink band-like plastic deformation zones in beams and combining with the measurement of kink band width in field outcrops, the thickness of strata governed by this criterion is quantitatively estimated, thereby achieving the quantification of the unit length in the maximum effective moment criterion. The results provide a theoretical basis for reconstructing stress-strain fields and analyzing deformation processes in related geological structures.

Key words: maximum effective moment criterion, elastoplastic beam, kink band, finite element method, COMSOL

刘天乐, 何涛. 基于弹塑性梁模型的最大有效力矩准则单元边长定量研究[J]. 北京大学学报（自然科学版）, 2026, 62(3): 571-580.

LIU Tianle, HE Tao. Quantitative Study on Unit Length of Maximum Effective Moment Criterion Based on Elastoplastic Beam Model[J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2026, 62(3): 571-580.

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链接本文: https://xbna.pku.edu.cn/CN/10.13209/j.0479-8023.2025.034

https://xbna.pku.edu.cn/CN/Y2026/V62/I3/571

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基于弹塑性梁模型的最大有效力矩准则单元边长定量研究

Quantitative Study on Unit Length of Maximum Effective Moment Criterion Based on Elastoplastic Beam Model

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